Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/9940
Title: On a combination method of VDR and patchwork for generating uniform random points on a unit sphere
Authors: Yang, Z
Pang, WK
Hou, SH
Leung, PK 
Keywords: Generation of uniform distribution
Patchwork method
Vertical density representation
Issue Date: 2005
Publisher: Elsevier Inc
Source: Journal of multivariate analysis, 2005, v. 95, no. 1, p. 23-36 How to cite?
Journal: Journal of Multivariate Analysis 
Abstract: In this paper, we use a combination of VDR theory and patchwork method to derive an efficient algorithm for generating uniform random points on a unit d-sphere. We first propose an algorithm to generate random vector with uniform distribution on a unit 2-sphere on the plane. Then we use VDR theory to reduce random vector Xd with uniform distribution on a unit d-sphere into Xd = (Xd-2, √1 - ∥Xd-2∥2 (Xd-1, Xd)), such that the random vector (Xd-1, Xd) is uniformly distributed on a unit 2-sphere and Xd-2 has conditional uniform distribution on a (d - 2)-sphere of radius √1 - V, given V = v with V having the p.d.f. d/2 (1 - v) d-2/2. Finally, we arrive by induction at an algorithm for generating uniform random points on a unit d-sphere.
URI: http://hdl.handle.net/10397/9940
ISSN: 0047-259X
DOI: 10.1016/j.jmva.2004.08.012
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